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Generalizations of the Landau–Hadamard inequality and inequalities for quadratic polynomials of operators

Published online by Cambridge University Press:  14 November 2011

Khr. N. Boyadzhiev
Khr. N. Boyadzhiev
Affiliation:
Faculty of Mathematics, University of Sofia, Sofia, Bulgaria
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Synopsis

We give generalizations of the Landau–Hadamard inequality ‖u′‖2 ≦ K ‖u‖ ‖u″‖ replacing u” by the second-order differential expression u″ − (α + β)u′ + αβu (α, β ∈ ℂ). The new functional inequalities are then used to obtain similar inequalities for dissipative and skew-Hermitian operators.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 1-2 , 1986 , pp. 123 - 129
Copyright
Copyright © Royal Society of Edinburgh 1986

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